I'd think that to use no apostrophe would be if you were using it as an adjective, as to replace with the original phrase the possibilities are

"Help for Kids' activites will start in the summer."
"Help for Kids activites will start in the summer."

The first one shows possession as was intended, the second one merely shows description. When you replace with the acronym you get

"HFK' activites will start in the summer."

but the phrase no longer ends in 's' so it must be changed, for the same reason that you add an 's' when using the possessive form of plurals that don't end in 's' (that is, you wouldn't refer to "all the mice' cheese," you'd refer to "all the mice's cheese").

This makes the correct form

"HFK's activites will start in the summer."

All in my humble opinion, of course. I'm sure there's better arguments for this phrase then mine, but this is how I would do it.